Pandas: transpose df and create multi-index using column names

Question

I have the following df:

            user  2019-01-01  2019-01-02  
0             Me         1.0         3.0 
1         Myself         2.0         2.0  
2      And_Irene         3.0         1.0  

I want to transform this into the following:

                        Count                       
2019-01-01  Me          1.0   
2019-01-01  Myself      2.0
2019-01-01  And_Irene   3.0    
2019-01-02  Me          3.0
2019-01-02  Myself      2.0
2019-01-02  And_Irene   1.0

I think this has to be done through df.T, but I am not sure what the next steps should be. Using df.T returns:

             0       1          2
user        Me  Myself  And_Irene
2019-01-01   1       2          3
2019-01-02   3       2          1

But then, how can I group the results using the column names? I am not sure this is the right way to do this.